Mechanism of synchronization in a random dynamical system

Details Mechanism of synchronization in a random dynamical system Mechanism of synchronization in a random dynamical system

2001-04-17

arxiv.org/abs/nlin/0104034v3

Nonlinear Sciences

Chaotic Dynamics

9 pages, 7 figures, To appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.64.036219

The mechanism of synchronization in the random Zaslavsky map is investigated. From the error dynamics of two particles, the structure of phase space was analyzed, and a transcritical bifurcation between a saddle and a stable fixed point was found. We have verified the structure of on-off intermittency in terms of a biased random walk. Furthermore, for the generalized case of the ensemble of particles, \emph{a modified definition} of the size of a snapshot attractor was exploited to establish the link with a random walk. As a result, the structure of on-off intermittency in the ensemble of particles was explicitly revealed near the transition.

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